How do you evaluate #4.24\times 4.24#?

1 Answer
George C.
Jan 15, 2017

#4.24 xx 4.24 = 17.9776#

Explanation:

Doing the calculation by hand, you could break it down as follows:

Starting with #4.24#, divide by #4# to get #1.06 = 1+0.06#

Then:

#4.24 xx 4.24 = 4 xx (1 + 0.06) xx 4 xx (1 + 0.06)#

#color(white)(4.24 xx 4.24) = 16 xx (1 + 0.06)^2#

#color(white)(4.24 xx 4.24) = 16 xx (1 + 2(0.06)+ 0.06^2)#

#color(white)(4.24 xx 4.24) = 16 xx (1 + 0.12 + 0.0036)#

#color(white)(4.24 xx 4.24) = 16 xx 1.1236#

#color(white)(4.24 xx 4.24) = 8 xx 2.2472#

#color(white)(4.24 xx 4.24) = 4 xx 4.4944#

#color(white)(4.24 xx 4.24) = 2 xx 8.9888#

#color(white)(4.24 xx 4.24) = 17.9776#

That may seem a little long-winded, but being able to double and halve numbers can often make arithmetic easier to do in your head.

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